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**Binomial distribution**

Use Cornell Notes

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**Setting For a binomial distribution**

Acronym is POTI Probability needs to be the same for all trials Outcomes---there are only two—success or failure Trials—there is a set number of them Independent—each trial is independent from one another.

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**Which of these situations are binomial?**

You observe the gender of the next 20 kids born at a hospital. The variable X is the number of girls among them. A couple decides to have children until they have a girl. The variable X is the number of total children born.

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Which is binomial? Phat is going to shoot 10 free throws. His coach is going to help him. Between every free throw Phat gets a few pointers. X is the number Phat makes. Jamaal buys a state lottery ticket each week. The variable X is the number of times a year that he wins.

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**Probabilities involving three children**

A couple wants to have three children and wonders about all the combinations. Construct a chart for this. Start with using the binomial theorem, and use Pascal’s triangle (.5X+.5Y)^3

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**Pascal’s Triangle—make this distribution chart**

1 2 3 .125 .375

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**Bobby(ie) is a 70% free throw shooter**

Bobby(ie) is a 70% free throw shooter. What is the probability in four shots that he/she makes at least three? 1 2 3 4 .0081 .0756 .2646 .4116 .2401

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Questions What is the expected number of free throws made in that situation? What is the mean of the free throw problem? Of the child problem? What is the standard deviation of the free throw problem? Of the child problem? Name two ways to find the standard deviation of the free throw problem.

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Application Karen is the school’s best player. She is also a 75% free throw shooter. She goes to the free throw line 12 times in the “big game” and makes seven. People say that she “choked.” how rare is it to make 7 out of 12? How about 7 or less out of 12? Based on these numbers, did she choke in your opinion?

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Did Karen Choke? On Calculator, make a binomial PDF and CDF chart? What do these mean? Make a histogram of Binomial PDF and CDF.—2nd stat plot…make X-L1 and the frequency L2.

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Did Karen Choke? What is the expected number of three throws she’d make? What is the standard deviation? Does that give you a hint as to whether or not she choked?

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**Should you guess on a multiple choice test?**

Take this test. There are five questions---(a-e) Make a distribution chart. 1 2 3 4 5 .32768 .4096 .2048 .0512 .0064 .00032

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Multiple choice What is the expected number of questions that you'd get right? What is the standard deviation? Make a histogram of the this situation for both binomial PDF and CDF.

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Section 6.3 Binomial Distributions. A Gaggle of Girls Let’s use simulation to find the probability that a couple who has three children has all girls.

Section 6.3 Binomial Distributions. A Gaggle of Girls Let’s use simulation to find the probability that a couple who has three children has all girls.

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